Circuits, Systems, and Signal Processing

, Volume 35, Issue 3, pp 933–951 | Cite as

Biorthogonal Multiwavelets with Sampling Property and Application in Image Compression

  • Baobin LiEmail author
  • Lizhong Peng


This paper discusses biorthogonal multiwavelets with sampling property. In such systems, vector-valued refinable functions act as the sinc function in the Shannon sampling theorem, and their corresponding matrix-valued masks possess a special structure. In particular, for the multiplicity \(r=2\), a biorthogonal multifilter bank can be reduced to two scalar-valued filters. Moreover, if the vector-valued scaling functions are interpolating, three different concepts: balancing order, approximation order and analysis-ready order, will be shown to be equivalent. Based on this result, we introduce the transferring armlet order for constructing biorthogonal balanced multiwavelets with sampling property. Also, some balanced biorthogonal multiwavelets will be obtained. Finally, application of biorthogonal interpolating multiwavelets in image compression is discussed. Experiments show that for the same length, the biorthogonal multifilter bank is superior to the orthogonal case. Moreover, certain biorthogonal interpolating multiwavelets are also better than the classical Daubechies wavelets.


Multiwavelet Biorthogonal multiwavelet  Analysis-ready multiwavelet Transferring armlet order 

Mathematics Subject Classification

42C40a 65T60 15A23 94A08 



The authors thank anonymous reviewers and the editor-in-chief, Prof. M.N.S.Swamy, for their valuable suggestions and comments for improving the presentation of this paper. This work was supported in part by NSFC under Grant No. 11301504 and in part by the President Fund of University of Chinese Academy of Sciences under Grant No. Y25101HY00.


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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.School of Computer and ControlUniversity of Chinese Academy of SciencesBeijingPeople’s Republic of China
  2. 2.School of Mathematical SciencesPeking UniversityBeijingPeople’s Republic of China

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